{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T16:19:29Z","timestamp":1704989969849},"reference-count":12,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,7,30]],"date-time":"2020-07-30T00:00:00Z","timestamp":1596067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,7,30]],"date-time":"2020-07-30T00:00:00Z","timestamp":1596067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2020,9]]},"DOI":"10.1007\/s00211-020-01137-9","type":"journal-article","created":{"date-parts":[[2020,7,30]],"date-time":"2020-07-30T07:42:44Z","timestamp":1596094964000},"page":"159-179","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Lower a posteriori error estimates on anisotropic meshes"],"prefix":"10.1007","volume":"146","author":[{"given":"Natalia","family":"Kopteva","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,7,30]]},"reference":[{"key":"1137_CR1","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032824","volume-title":"A Posteriori Error Estimation in Finite Element Analysis","author":"M Ainsworth","year":"2000","unstructured":"Ainsworth, M., Oden, J.T.: A Posteriori Error Estimation in Finite Element Analysis. Wiley, New York (2000)"},{"key":"1137_CR2","doi-asserted-by":"publisher","first-page":"2519","DOI":"10.1137\/140983458","volume":"53","author":"N Kopteva","year":"2015","unstructured":"Kopteva, N.: Maximum-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes. SIAM J. Numer. Anal. 53, 2519\u20132544 (2015)","journal-title":"SIAM J. Numer. Anal."},{"key":"1137_CR3","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1007\/s00211-017-0889-3","volume":"137","author":"N Kopteva","year":"2017","unstructured":"Kopteva, N.: Energy-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes. Numer. Math. 137, 607\u2013642 (2017)","journal-title":"Numer. Math."},{"key":"1137_CR4","unstructured":"Kopteva,\u00a0N.: Fully computable a posteriori error estimator using anisotropic flux equilibration on anisotropic meshes. arXiv:1704.04404 (2017)"},{"key":"1137_CR5","doi-asserted-by":"crossref","unstructured":"Kopteva,\u00a0N.: Lower a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes (in preparation) (2020)","DOI":"10.1007\/978-3-030-41800-7_9"},{"key":"1137_CR6","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1007\/s002110000170","volume":"86","author":"G Kunert","year":"2000","unstructured":"Kunert, G.: An a posteriori residual error estimator for the finite element method on anisotropic tetrahedral meshes. Numer. Math. 86, 471\u2013490 (2000)","journal-title":"Numer. Math."},{"key":"1137_CR7","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1023\/A:1014248711347","volume":"15","author":"G Kunert","year":"2001","unstructured":"Kunert, G.: Robust a posteriori error estimation for a singularly perturbed reaction-diffusion equation on anisotropic tetrahedral meshes. Adv. Comput. Math. 15, 237\u2013259 (2001)","journal-title":"Adv. Comput. Math."},{"key":"1137_CR8","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/PL00005407","volume":"86","author":"G Kunert","year":"2000","unstructured":"Kunert, G., Verf\u00fcrth, R.: Edge residuals dominate a posteriori error estimates for linear finite element methods on anisotropic triangular and tetrahedral meshes. Numer. Math. 86, 283\u2013303 (2000)","journal-title":"Numer. Math."},{"key":"1137_CR9","doi-asserted-by":"publisher","first-page":"799","DOI":"10.1016\/j.cma.2005.02.009","volume":"195","author":"S Micheletti","year":"2006","unstructured":"Micheletti, S., Perotto, S.: Reliability and efficiency of an anisotropic Zienkiewicz-Zhu error estimator. Comput. Methods Appl. Mech. Eng. 195, 799\u2013835 (2006)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"1137_CR10","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1002\/cnm.546","volume":"19","author":"M Picasso","year":"2003","unstructured":"Picasso, M.: Numerical study of the effectivity index for an anisotropic error indicator based on Zienkiewicz-Zhu error estimator. Commun. Numer. Methods Eng. 19, 13\u201323 (2003)","journal-title":"Commun. Numer. Methods Eng."},{"key":"1137_CR11","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199679423.001.0001","volume-title":"A Posteriori Error Estimation Techniques for Finite Element Methods","author":"R Verf\u00fcrth","year":"2013","unstructured":"Verf\u00fcrth, R.: A Posteriori Error Estimation Techniques for Finite Element Methods. Oxford University Press, Oxford (2013)"},{"key":"1137_CR12","doi-asserted-by":"publisher","first-page":"1139","DOI":"10.1090\/S0025-5718-03-01600-4","volume":"73","author":"J Xu","year":"2004","unstructured":"Xu, J., Zhang, Z.: Analysis of recovery type a posteriori error estimators for mildly structured grids. Math. Comput. 73, 1139\u20131152 (2004)","journal-title":"Math. Comput."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-020-01137-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00211-020-01137-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-020-01137-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,29]],"date-time":"2021-07-29T23:15:34Z","timestamp":1627600534000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00211-020-01137-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,30]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["1137"],"URL":"https:\/\/doi.org\/10.1007\/s00211-020-01137-9","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,7,30]]},"assertion":[{"value":"13 July 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 February 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 July 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}